How do Power and Strength values correlate?
I did some testing. You can use this as a reference sheet :).


  Power : Strength ratio is 10:2,5 (for 1m² area)



Area lights use Power (W), Mesh lights use Strength
Mesh light used - default plane with Emission shader




Intensity and size relationship


Area lights - maintain their intensity with increased size.
Mesh lights - increase their intensity with increased size




Power:Strength reference sheet  


I tested these as 4096x4096 images and still couldn't tell the difference.
Sorry for the color banding and compression artifacts.
Noise is a tiny bit higher for Mesh lights.